10th Biennial International Conference & Exposition
P 300
Well logs driven Initial Velocity Model building for Depth Imaging:
-A Geostatistical Approach
Vishnoi D K*, Lavendra Kumar, A C Mandal, Srilata Mohapatra, D Chatterjee
Summary
For depth imaging, there are two main issues: one is to have a good migration algorithm and secondly the accurate rather
realistic velocity model. Kirchhoff’s migration algorithm is widely used in the industry unless some specific requirement. For
getting a correct and accurate imaging, we should have a good initial velocity model for any time/depth imaging. Different
methods /approaches are being used in the industry today to get initial model. It is a common practice to start with Dix
converted velocities from our available RMS velocities. Second approach is making use of these RMS velocities, constrained
with external trend of structural models and formation volume to get initial model through constrained velocity inversion
(CVI), (Koren, Z. et al., 2005). Coherency inversion based on layer stripping method is the other approach for getting the
initial model where ray bending comes into the picture (Landa, E., et al., 1991). In current study, an alternative approach
using well logs (sonic) and RMS velocities with preliminary structural maps in depth domain was used to get an integrated
depth interval velocity volume which is based on Geostatistical Kriging interpolation technique. This volume was used as
initial velocity model which subsequently updated with tomographic iterations to achieve final velocity model for imaging.
This approach was tested on a subset project of West Coast of India which has many layers of high velocity carbonates. The
results were found quite encouraging. The initial model follows the high/low velocity trends as per well logs where well data
is available. The approach and its results on real data are discussed in this study.
Keywords: Geostatistical, Initial velocity model, PSDM Summary
been carried out using Paradigm Suite of software after
taking a demo license from Paradigm.
Introduction
The Geostatistical method uses layered structures in 3D to
create volumes, by performing 3D Micro-structure Kriging
to interpolate between well logs and/or vertical velocity
functions. This is generally better when dealing with
geological structures in 3D. Input could be well logs,
vertical velocity functions, maps, or a formation volume.
The 3D structure can be defined using constant time/depth
values, time migrated or depth 3D model maps, or
formation volumes as input. This approach was attempted
on a small subset of volume from West Coast of India
where lot of velocity anomalies were to be answered.
Initial model was built up using 8 wells in the area where
sonic logs were available. These logs were available only
up to drilled depth or above and not for entire length of
seismic. Therefore, vertical functions (RMS) were used in
the zones where logs were not available. This approach has
Theory
To obtain the statistically optimal interpolation of input
data, interpolation method based on Kriging is used. The
interpolation method known as Kriging (named after its
developer, Daniel G. Krige) to obtain the statistically
optimal interpolation of input data. According to Geoff
Bohling, Kriging is “Optimal interpolation based on
regression of observed z values of surrounding data points,
weighted according to spatial covariance values”. Kriging
is based on the assumption that there is a spatial
dependency between geological properties at separate
points in an area and this spatial dependency is a function
of the distance between the points. The statistical measure
that expresses the rate of change in point values in relation
to distance is the semi-variance. Semivariances are
SPIC, ONGC, Mumbai
[email protected]
calculated for different distances between points and the
results are plotted in a semi-variogram, which is then used
for calculating the weighting coefficients for Kriging
interpolation. The semivariogram (Fig-2) determines the
extent of variance of an unknown value of one point from
the known value of a different point, depending upon its
distance from the known point. Kriging interpolation in
GeoStatistics volume creation is performed in two stages:
•
•
Calculating an optimal semi-variogram from well
data.
Kriging (calculating the weight coefficients for
each control point) and interpolation of the data.
Kriging requires the calculation of a semi-variogram
model. The semi-variogram is calculated from the well log
or vertical function data, and it contains information on the
variance of the data as a function of distance from the
wells. Therefore, the semi-variogram requires at least one
log.
Layer geometries are defined by selecting the maps for top
and bottom boundaries. Constant time and depth values for
top and bottom boundaries may be used for defining the
layer geometry. The internal geometry of any layer may be
defined either parallel to top /bottom, proportional, planar
parallel to external map. (Fig-1).
Fig-2: Semi variogram model
Methodology
The inputs required in this method are sonic logs, vertical
functions (RMS) and structural maps. The logs usually
contain very high frequencies which need to be de-spiked
and filtered out before use. It starts with defining of layer
geometry by selecting maps for top and bottom
boundaries, constant time and depth values for top and
bottom boundaries, or selection of a layer in a formation
volume. The generalized work flow of this method is
shown at (Fig-3).
Fig-3 Work flow for creation of velocity model derived from
Geostatistical approach
Fig-1: Defining a type of layer geometry
In current study, eight layers (top 2 layers: Vertical
functions, next 4 layers: sonic logs, and rest 2 layers: again
vertical functions) with layer topology parallel to bottom
defines the layer geometry. RMS velocities (vertical
functions) were used from water bottom to layer H1A and
from layer H4 to end. Second part of this work flow uses
well (Sonic logs) data for layers H1A, H2B, H3A & H4 for
deriving interval velocity from sonic logs. Next step is
calculating semi-variogram models for Ordinary Kriging
method used for interpolation for each layer. For ordinary
Kriging, rather than assuming that the mean is constant
over the entire domain, we assume that it is constant in the
local neighbourhood of each estimation point. At least two
well logs must intersect with the layer to produce a semi
variogram. One by one layer is added, interpolated and
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saved before going to next layer. Here multi well logs were
used to create a semi-variogram from input data.
is saved and updated with another layer to be added if any
(Fig-4). With this approach, initial depth interval velocity
model was obtained which shows the trend of velocity as
per sonic log (filtered) variations (Fig-5).
Results & Discussion
Results are based on the work carried out over a small
volume of western offshore Basin where 8 wells were
available with main markers from H1A (Bandra), H2B
(Bombay), H3A (Mukta) and H4 (Panna) along with
Fig-6A PSDM gather using initial velocity model created with
Geostatistical approach
Fig-4 Kriging results in view: Interval velocity slice, inline/ xline
sections for layer by layer till all layers
Fig-6B PSDM gather using initial velocity model created
with conventional approach
Fig-5
Initial depth interval velocity model with sonic Log
(filtered) overlaid for four markers
Before performing Kriging, customization of volume
parameters is required. After Kriging, smoothened section
image is available for preview before creating and saving
the output volume for a single layer. Each iteration of
above work flow adds another layer to the volume which
many layers of high/low velocity carbonate layers in
between till basement. The PSDM gathers after initial
KPSDM were found not so flat (Fig-6A) as in case of
Dix/CVI approach (Fig-6B) where gathers were nearly
flat. The reason being, the velocity where log data has been
considered is not suitable for seismic imaging but
represents the nearly true vertical velocity required for
correct depth. The final anisotropic velocity model was
created using Geostatistical approach as above followed by
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six tomographic iterations.
The result of anisotropic
PSDM, the output gather shows the flat response (Fig7A)
using this volume. These gathers shows better depth and
flat response compare to without use of log data in initial
model. The results of anisotropic PSDM using
conventional velocity model after tomographic inversions
are also shown for comparison (Fig-7B). The initial as well
as final depth interval velocity model shows the variations
as per trend of log data (Fig-8) which was not seen in the
model arrived from without use of log data (Fig-9). The
variations as per log details have answered the many
velocity related issues in the area.
Fig-9 Depth interval velocity model without use of sonic log after
tomographic inversions unable to account the fine interval
velocity
Conclusion
Fig-7A PSDM gather using final velocity model created with
Geostatistical approach after tomographic iterations

The preliminary study suggests about the
dependency on log data and its judicious use in
velocity model building.

The initial velocity section/volume shows the
detailed variation in the depth interval velocities
as per the trend of the log.

Final velocity section/volume also confirms the
trend of log which explains the changes in
lithology within the layer matrix initially taken.
Interval velocity attribute will now provide value
addition in Exploration.

The approach seems to be more appropriate in
terms of layer definitions and its variation
throughout the volume

This approach is not limited to depth domain but
works well for time domain also to get interval
velocity volume in time which is normally the
requirement for curved rays’ migration.

It could be more accurate when more no of well
logs up to its full length/ zone of interest are to
be included for Kriging.

Fine tuning of velocity model and depth relation
using one or two well tie tomographic inversions
will be an added advantage.
Fig-7B PSDM gather using final velocity model created without
Geostatistical approach after tomographic iterations
Acknowledgement
Fig-8 Final depth interval velocity model with sonic log (filtered)
overlaid after tomographic inversions shows Inter layer
variations as per log variation
Authors wish their sincere thanks to Director
(Exploration), ONGC for giving permission to publish
and present this paper in SPG Conference 2013 at Kochi.
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Authors are also thankful to Shri P K Bhowmick,
EDCOED, WOB, and ONGC Mumbai for providing
opportunity to carry out this study which may be helpful
for exploration. Authors wishes to acknowledge the
sincere support of their fellow colleagues who helped
directly or indirectly to carry out this analysis. Authors are
also thankful to M/s Paradigm Geophysical for providing
the demo license of Geostatistical tool and Tomofacilitator to carry out this study.
Views expressed here are those of the authors only and do not
reflect the views of the Organization which they belong to.
References
Geoff Bohling, KRIGING, C&PE 940, 19 October 2005
Koren, Z. and Rawe, I. (2005) “Constrained velocity
inversion”, SEG Expanded abstract, 22892292
Landa, E., Thore, P., Sorin, V., and Koren, Z. (1991).
”Interpretation of velocity estimates from Coherency
inversion.” GEOPHYSICS, 56(9), 1377–1383
Model based depth imaging by Stuart Fugin, course note
series No 10 (SEG)
Online help of Paradigm documentation
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